Consider all ordered pairs of integers \((x,y)\) such that \[\frac{5}{x}+\frac{7}{y} = \frac{12}{xy}.\]

The smallest positive integer value of \(x\) in these ordered pairs is \(1,\) since \(x=y=1\) satisfies the equation. What is the second smallest positive integer value of \(x\) in these ordered pairs?